let V be RealLinearSpace; :: thesis: for u, v, w being VECTOR of V st {u,w,v} is linearly-independent & u <> v & u <> w & v <> w holds
{u,(- w),(- v)} is linearly-independent
let u, v, w be VECTOR of V; :: thesis: ( {u,w,v} is linearly-independent & u <> v & u <> w & v <> w implies {u,(- w),(- v)} is linearly-independent )
( - v = (- 1) * v & - w = (- 1) * w ) by RLVECT_1:16;
hence ( {u,w,v} is linearly-independent & u <> v & u <> w & v <> w implies {u,(- w),(- v)} is linearly-independent ) by Th28; :: thesis: verum